Abstract
In this paper, we examine the Ruelle-type spectral functions [Formula: see text], which define an overall description of the content of the work. We investigate the GopakumarâVafa reformulation of the string partition functions, describe the [Formula: see text] LandauâGinzburg model in terms of Ruelle-type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in [Formula: see text] theories, construct the functional equations for [Formula: see text], and analyze the modular transformation laws for the elliptic genus of the LandauâGinzburg model and study their properties in details.
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